Spin-wave-induced correction to the conductivity of ferromagnets

Abstract

We calculate the correction to the conductivity of a disordered ferromagnetic metal due to spin-wave-mediated electron-electron interactions. This correction is the generalization of the Altshuler-Aronov correction to spin-wave-mediated interactions. We derive a general expression for the conductivity correction to lowest order in the spin-wave-mediated interaction and for the limit that the exchange splitting $\ensuremath{\Delta}$ is much smaller than the Fermi energy. For a ``clean'' ferromagnet with $\ensuremath{\Delta}{\ensuremath{\tau}}_{\mathrm{el}}/\ensuremath{\hbar}\ensuremath{\gg}1$, with ${\ensuremath{\tau}}_{\mathrm{el}}$ being the mean time for impurity scattering, we find a correction $\ensuremath{\delta}\ensuremath{\sigma}\ensuremath{\propto}\ensuremath{-}{T}^{5/2}$ at temperatures $T$ above the spin-wave gap. In the opposite, ``dirty'' limit, $\ensuremath{\Delta}{\ensuremath{\tau}}_{\mathrm{el}}/\ensuremath{\hbar}\ensuremath{\ll}1$, the correction is a nonmonotonous function of temperature.